Auth: Vidar Thomée
Book Summary: This graduate-level text provides a comprehensive mathematical analysis of the Galerkin finite element method applied to parabolic partial differential equations, which typically govern time-dependent diffusion processes like heat conduction.
The book focuses on rigorous error estimation and stability analysis for both spatial discretization and time-stepping schemes. It covers standard piecewise linear approximations, high-order methods, and specialized topics such as maximum-norm error estimates, smoothing properties, and problems with rough initial data. It serves as an essential reference for applied mathematicians and numerical analysts seeking a deep theoretical understanding of how evolutionary equations behave under finite element discretization.
